I have an iPhone 3G with iOS 4.1, but don't have an Apple ID. I just got this used phone recently. It is jailbroken and unlocked to work on T-Mobile. I looked on the app store and noticed some apps that required a higher iOS. Looking online, I edited SystemVersion.plist with iFile to make the system think I have iOS 5.1. The app store worked perfectly then (still don't have an ID). Then I tried to get even higher to iOS 6.1.1, but I noticed the app store was all gray. I tried to put the iOS back to 4.1, but the problem persisted. I am unable to restore the phone. Is there any backup or other solution to this problem I could use?
Have you tried resetting settings?
Settings > General > Reset > Reset All Settings
If that doesn't fix your problem, try signing in to the App Store. I believe you can do this from the Settings > Store menu.